## anonymous one year ago In parallelogram PQRS, find the height h. Then calculate the area of PQRS.

1. mathstudent55

In a paralleogram, what do you know about opposite angles?

2. anonymous

|dw:1437449376951:dw|

3. anonymous

@mathstudent55 ∠R=45, ∠S=180-45=135, ∠P=45,and ∠Q=135.

4. mathstudent55

Correct. Opposite angles are congruent. |dw:1437450112404:dw|

5. mathstudent55

That makes the small triangle on the left side a 45-45-90 triangle.

6. mathstudent55

|dw:1437450166044:dw|

7. mathstudent55

Since you have a 45-45-90 triangle, you can use the ratio of the length of the sides of a 45-45-90 triangle to find h.

8. mathstudent55

Do you know the ratio of the sides of a 45-45-90 triangle?

9. anonymous

1 to 1

10. anonymous

$\sqrt{2}$

11. mathstudent55

Yes, $$1 : 1 : \sqrt 2$$ The hypotenuse is $$\sqrt 2$$ times the length of either leg. The legs are congruent. The height of the parallelogram is the leg of the right triangle. What is the length of the leg?

12. anonymous

8

13. mathstudent55

Correct. Now you know the height of the parallelogram is 8. Do you know how to find the area of a parallelogram?

14. mathstudent55

$$\Large A_{parallelogram} = bh$$ where b = length of base, and h = height.

15. mathstudent55

You were given a base of 20 cm, and you calculated a height of 8 cm.

16. anonymous

A=bh. So A=20x8= 160cm^2

17. mathstudent55

@SimiYami Do you understand how to find the area?

18. anonymous

Yes, thank you for the help @mathstudent55. This is the exact answer in my book :D

19. mathstudent55

You're welcome.